Alpharabian tuning: Difference between revisions

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* Intervals that result from the modification of a Pythagorean interval by [[1089/1024]] are labeled similarly to those modified in the equivalent fashion by [[2187/2048]], the only difference being that modification by 1089/1024 results in an Alpharabian interval rather than a Pythagorean interval.

* Since 1089/1024 is (33/32)^2, modifying a Pythagorean interval by [[33/32]] always results in an interval that is considered Alpharabian.

* As both the [[243/242|rastma]] and [[1331/1296]] are [[Diatonic, Chromatic, Enharmonic, Subchromatic|subchromas]] that form differences between members of the 2.11 subgroup and Pythagorean intervals, both of these subchromas belong to a set of intervals defining different interval sets within Alpharabian tuning, and subchromas within this particular interval set help define the differences between Pythagorean, Alpharabian and ~~Betarabian intervals~~.

The following premise has currently not been finalized:

* As both the [[243/242|rastma]] and [[1331/1296]] are [[Diatonic, Chromatic, Enharmonic, Subchromatic|subchromas]] that form differences between members of the 2.11 subgroup and Pythagorean intervals, both of these subchromas belong to a set of intervals defining different interval sets within Alpharabian tuning, and subchromas within this particular interval set help define the differences between intervals classified as Pythagorean, Alpharabian, Betarabian and so forth.

The following rules are directly derived from the above premises:

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:* Augmentation of a Perfect Fourth or Perfect Fifth by 33/32 results in a Paramajor interval

:* Dimunition of a Perfect Fourth or Perfect Fifth by 33/32 results in a Paraminor interval

:* Augmentation of a Pythagorean Minor interval by 33/32 results in ~~a Lesser Neutral~~ interval

:* Augmentation of a Pythagorean Minor interval by 33/32 results in an Artoneutral interval

:* Dimunition of a Pythagorean Major interval by 33/32 results in a ~~Greater Neutral~~ interval

:* Dimunition of a Pythagorean Major interval by 33/32 results in a Tendoneutral interval

The following rules are more questionable as they rely on the aforementioned questionable premise:

* Generally, intervals that result that result from the modification of a Pythagorean interval by 1331/1296 take either the 'super' or 'sub' prefixes, with these prefixes generally being stacked where multiple such modifications occur, however, there are some significant caveats...

:* Augmentation of a Pythagorean Minor interval by a single 1331/1296 results in a Supraminor interval, but a second such augmentation results in a Betarabian Major interval due to said interval differing from the nearby Alpharabian Major (covered under modifications by 1089/1024) by a rastma.

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 * Intervals that result from the modification of a Pythagorean interval by [[1089/1024]] are labeled similarly to those modified in the equivalent fashion by [[2187/2048]], the only difference being that modification by 1089/1024 results in an Alpharabian interval rather than a Pythagorean interval.
 * Since 1089/1024 is (33/32)^2, modifying a Pythagorean interval by [[33/32]] always results in an interval that is considered Alpharabian.
-* As both the [[243/242|rastma]] and [[1331/1296]] are [[Diatonic, Chromatic, Enharmonic, Subchromatic|subchromas]] that form differences between members of the 2.11 subgroup and Pythagorean intervals, both of these subchromas belong to a set of intervals defining different interval sets within Alpharabian tuning, and subchromas within this particular interval set help define the differences between Pythagorean, Alpharabian and Betarabian intervals.
+The following premise has currently not been finalized:
+* As both the [[243/242|rastma]] and [[1331/1296]] are [[Diatonic, Chromatic, Enharmonic, Subchromatic|subchromas]] that form differences between members of the 2.11 subgroup and Pythagorean intervals, both of these subchromas belong to a set of intervals defining different interval sets within Alpharabian tuning, and subchromas within this particular interval set help define the differences between intervals classified as Pythagorean, Alpharabian, Betarabian and so forth.
 The following rules are directly derived from the above premises:
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 :* Augmentation of a Perfect Fourth or Perfect Fifth by 33/32 results in a Paramajor interval
 :* Dimunition of a Perfect Fourth or Perfect Fifth by 33/32 results in a Paraminor interval
-:* Augmentation of a Pythagorean Minor interval by 33/32 results in a Lesser Neutral interval
+:* Augmentation of a Pythagorean Minor interval by 33/32 results in an Artoneutral interval
-:* Dimunition of a Pythagorean Major interval by 33/32 results in a Greater Neutral interval
+:* Dimunition of a Pythagorean Major interval by 33/32 results in a Tendoneutral interval
+The following rules are more questionable as they rely on the aforementioned questionable premise:
 * Generally, intervals that result that result from the modification of a Pythagorean interval by 1331/1296 take either the 'super' or 'sub' prefixes, with these prefixes generally being stacked where multiple such modifications occur, however, there are some significant caveats...
 :* Augmentation of a Pythagorean Minor interval by a single 1331/1296 results in a Supraminor interval, but a second such augmentation results in a Betarabian Major interval due to said interval differing from the nearby Alpharabian Major (covered under modifications by 1089/1024) by a rastma.